How do I turn y is greater than or equal to 10 - x into y is greater than or equal to mx + b?
Understand the Problem
The question is asking how to convert the inequality 'y is greater than or equal to 10 - x' into the slope-intercept form 'y is greater than or equal to mx + b'. This involves rearranging the inequality to isolate y on one side.
Answer
The inequality in slope-intercept form is \( y \geq x + 10 \).
Answer for screen readers
The inequality in slope-intercept form is ( y \geq x + 10 ).
Steps to Solve
- Start with the original inequality
We need to convert the inequality ( y \geq 10 - x ).
- Rearrange the inequality
To isolate ( y ), we can add ( x ) to both sides of the inequality. This gives us:
$$ y \geq 10 + x $$
- Rewrite in slope-intercept form
This form resembles ( y \geq mx + b ), where ( m ) is the slope and ( b ) is the y-intercept. Here, we can see that:
- ( m = 1 ) (the coefficient of ( x ))
- ( b = 10 )
Thus, the final slope-intercept form is:
$$ y \geq 1x + 10 $$
The inequality in slope-intercept form is ( y \geq x + 10 ).
More Information
This inequality represents a region that includes all points on or above the line ( y = x + 10 ). The slope of the line is 1, indicating that for every unit increase in ( x ), ( y ) increases by the same amount.
Tips
- Forgetting to reverse the inequality sign when multiplying or dividing by a negative number.
- Misplacing the terms when rearranging the inequality, leading to incorrect coefficients.
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